TY - JOUR

T1 - On two approaches to classification of higher local fields

AU - Ivanova, O.

AU - Vostokov, S.

AU - Zhukov, I.

N1 - O. Ivanova, S. Vostokov, I. Zhukov, “On two approaches to classification of higher local fields”, Chebyshevskii Sb., 20:2 (2019), 186–197

PY - 2019

Y1 - 2019

N2 - This article links Kurihara's classification of complete discrete valuation fields and Epp's theory of elimination of wild ramification.For any complete discrete valuation field K with arbitrary residue field of prime characteristic one can define a certain numerical invariant Γ(K) which underlies Kurihara's classification of such fields into 2 types: the field K is of Type I if and only if Γ(K) is positive. The value of this invariant indicates how distant is the given field from a standard one, i.e., from a field which is unramified over its constant subfield k which is the maximal subfield with perfect residue field. (Standard 2-dimensional local fields are exactly fields of the form k{{t}}.)We prove (under some mild restriction on K) that for a Type I mixed characteristic 2-dimensional local field K there exists an estimate from below for [l:k] where l/k is an extension such that lK is a standard field (existing due to Epp's theory); the logarithm of this degree can be estimated linearly in terms of Γ(K) with the coefficient depending only on eK/k.

AB - This article links Kurihara's classification of complete discrete valuation fields and Epp's theory of elimination of wild ramification.For any complete discrete valuation field K with arbitrary residue field of prime characteristic one can define a certain numerical invariant Γ(K) which underlies Kurihara's classification of such fields into 2 types: the field K is of Type I if and only if Γ(K) is positive. The value of this invariant indicates how distant is the given field from a standard one, i.e., from a field which is unramified over its constant subfield k which is the maximal subfield with perfect residue field. (Standard 2-dimensional local fields are exactly fields of the form k{{t}}.)We prove (under some mild restriction on K) that for a Type I mixed characteristic 2-dimensional local field K there exists an estimate from below for [l:k] where l/k is an extension such that lK is a standard field (existing due to Epp's theory); the logarithm of this degree can be estimated linearly in terms of Γ(K) with the coefficient depending only on eK/k.

KW - Higher local fields

KW - wild ramification

UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cheb&paperid=762&option_lang=eng

M3 - Article

VL - 20

SP - 186

EP - 197

JO - Chebyshevskii Sbornik

JF - Chebyshevskii Sbornik

SN - 2226-8383

IS - 2

ER -